Answer:
x=2, -4, -1
Step-by-step explanation:
-x³-3x²+6x+8=0
Multiply entire equation by -1:
x³+3x²-6x-8=0
Since x=2 is a solution, then x-2 must be a factor. Then:
x³+3x²-6x-8/x-2=x²+5x+4
x²+5x+4=0
Factor this:
x²+5x+4=(x+4)(x+1)=0
x=-4, -1
x=2, -4, -1
The slope of line CD is 0, making the function equal to y = 6
Didn't you mean y = ax^2? "^" denotes "exponentiation."
The first derivative of y = ax^2 represents the slope of the tangent line to the curve of y = ax^2. Here, dy/dx = 2ax. When x = 2, dy/dx = 2a(2) = 4a.
The point of tangency is (2,y), where y = a(2)^2, or y=4a; thus, the point of tangency is (2,4a). The equation of the tangent line to y=ax^2 at (2,4a) is found by (1) differentiating y=ax^2 with respect to x, (2) letting x = 2 in the result: dy/dx = 2ax => dy/dx (at 2,4a) = 2a(2) = 4a
The line 2x + y = b is supposed to be tangent to y = ax^2 at (2,4a).
The slope of 2x + y = b is found by solving 2x + y = b for y:
y = b - 2x => slope m = -2
Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2. All we have to do now is to find the value of b. We know that 2x + y = b, so if x=-2 and y=-8,
2(-2) + [-8] = b = -4 - 8 = -12
Thus, the equation of the parabola is y = ax^2 = (-1/2)x^2.
a = -2 and b = -8 are the required a and b values.
Answer:
a) 3.6%
Step-by-step explanation:
The given question mixed up, below is the correct question:
The bumper car ride at the state fair has 2 red cars, 4 green cars, and 2 blue cars. Garth is first in line for the ride and is assigned a car at random. Patty is next in line and is randomly assigned a car. Find the probability that both events A and B occur. Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Calculation:
Given that the state fair has 2 red cars, 4 green cars and 2 blue cars.
There are therefore 2+4+2 = 8 cars in total.
Probability that Events A occurs P(A) = 
= 4
Probability that Events B occurs P(B) = 
Probability that Events A and B occur P(A ∩ B) = × = 
= 0.0357 = 3.57% ≈ 3.6%
Therefore, the probability that both events A and B occur is 3.6%
